Physiological nutrient use efficiency (Steps 3 and 4)

The two approaches for deriving PhEmin and PhEmax are illustrated in Fig. 3.1 (Approach 1, not HI related) and Fig. 3.3 (Approach 2, HI related). In Approach 1, PhEmin and PhEmax values (Fig. 3.1) represent 2.5 and 97.5th _{percentiles of all points} and correspond to the boundary line for maximum accumulation (Ya) and for

maximum dilution (Yd) respectively. The six site/year combinations have different

positions in the envelopes, with Kumasi 2008 being closer to the boundary line for maximum dilution (Yd) for N (Fig. 3.1a) and K (Fig. 3.1c), and Nyankpala closer to the

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scatter graph of P uptake and roots yield (Fig. 3.1b) are closer together than those for N and K (Figs 3.1a and 3.1c, respectively), especially at low P uptake.

Fig. 3.2. Uptake of N (a), P (b) and K (c) as calculated in Step 2 in relation to observed uptake, and the associated regression line. Input variables for Step 2 were the soil and input supplies of nutrients estimated in Step 1. Each point represents the average observed uptake of eight values (four replicates, two seasons).

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In Approach 2, the HI and minimum and maximum mass fractions in roots and tops (Table 3.4) were used in Eqs. 3.6 and 3.7 to derive PhEmax and PhEmin (Table 3.5). Measured root nutrient mass fractions were generally within the ranges given by Nijhof (1987). Fig. 3.3 shows that PhE varies with HI across sites and years. It also shows that PhE of N was small compared with literature since all points are situated between PhEmed and PhEmin of Nijhof (1987). Fig. 3.3 also shows that PhE of P is within a comparable range across the three sites, and that PhE of K is generally large at Davié and Kumasi but small at Nyankpala, pointing out large K supply at the latter site. Furthermore, the largest values of PhE of K were achieved at high HI values, and vice versa, indicating that PhE of K increases with HI.

The comparison of the two approaches to determine PhEmin and PhEmax suggested that Approach 2 worked better at Davié and Kumasi (Table 3.6). Although the performances of the two approaches were comparable in terms of R2_{, Approach 2}

provided more accuracy in the prediction with smaller RMSE and NRMSE, and a Willmott index closer to 1. These results stress the importance of accounting for the influence of HI on PhEmax and PhEmin in predicting cassava yields.

Model performance was best for Davié with calculated and observed yields scattered around the 1:1 line and poorest for Nyankpala with an overestimation of observed yields by the model (Fig. 3.4). Since average values of HI were used by QUEFTS whereas HI varied over seasons, observed yields were overestimated in case the real HI was smaller than the average HI, and underestimated in case the real HI was larger than the average HI. At Nyankpala, calculated yields were much larger than observed yields (Figs 3.4 and 3.5). This is in agreement with the low PhE values observed at this site, which suggests an inefficient use and luxury uptake of nutrients. Planting was late in Nyankpala in the first year (June 29, 2007), whereas the rainy season ran from April to October, meaning that the crop benefited from four months of rain at most. The second half of the growing season the crop likely suffered from drought, causing a low PhE.

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Fig. 3.3. Physiological nutrient use efficiency (PhE) of N, P and K in relation to harvest index (HI). PhEmax and PhEmin represent physiological nutrient use efficiency at maximum dilution and maximum accumulation, respectively, and PhEmed the medium value between PhEmax and PhEmin. Each point is calculated with Eq. 3.6, Eq. 3.7 and measured nutrient mass fractions of both cultivars combined (Table 3.4). It represents the average of four replicates. Nijhof curves were also based on these equations, but with nutrient mass fractions from Nijhof (1987) (Table 3.4).

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Table 3.4. Ranges between 2.5th and 97.5th percentiles of nutrient mass fractions (g nutrient

kg−1 _{DM) in cassava roots and tops, as found in literature (Nijhof 1987) and in the present} study for each cultivar and both cultivars combined.

Source Roots Tops

N P K N P K

Nijhof 2.0 – 9.0 0.8 - 2.4 3.0 – 14.0 5.0 – 18.0 0.9 -5.5 4.5- 18.0

Gbazekoute 2.8 – 5.1 0.7– 1.7 2.8 – 7.7 7.9 – 12.8 0.9 – 1.7 3.5 – 9.5

Afisiasi 2.5 – 6.9 0.8 – 1.5 3.0 – 11.0 7.9 – 18.4 1.2- 2.8 3.4 – 19.8

Both cultivars 2.5 – 6.6 0.8 – 1.5 2.8 – 11.0 7.9 – 17.9 0.9 – 2.8 3.4 – 18.8

Table 3.5. The HI and the corresponding PhEmin and PhEmax used in model calculations. The abbreviations par and ver stand for parameterisation and verification experiments. To allow comparison with values found in India (Byju et al. 2012), PhE values were also calculated for a hypothetical cultivar with an HI of 0.40.

Cultivar HI PhEmin PhEmax

N P K N P K Gbazekoute-par 0.50 41 232 34 96 589 160 Gbazekoute-ver 0.55 47 262 38 112 653 178 Afisiafi-par 0.65 61 329 47 148 782 214 Afisiafi-ver 0.70 70 365 53 170 848 233 Hypothetical 0.40 30 175 26 70 465 126 India 0.40 35 250 32 80 750 102

Table 3.6. The ability of QUEFTS to predict observed yields using two different approaches to derive PhEmin and PhEmax. Slope and R² are relative to the linear regression line between calculated (y-axis) and measured (x-axis) yields. The number of observations per site was 20, with replicates averaged per season.

PhE boundary lines approaches Parameter Davié Nyankpala Kumasi

Approach 1: Yield to uptake ratio Slope 1.28 1.42 0.86

R² 0.84 0.85 0.69

RMSE (kg ha−1_{) 4226 3046 1843}

NMSE (%) 32 47 18

Willmott’s index 0.742 0.690 0.872

Approach 2: HI related PhEmin & PhEmax Slope 1.00 1.55 0.95 R² 0.82 0.85 0.67 RMSE (kg ha−1_{) 1702 3941 1354} NMSE (%) 13 60 13 Willmott’s index 0.932 0.604 0.930

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Fig. 3.4. Relations between yields calculated with Step 3 and 4 of QUEFTS using HI related PhE boundary lines (Approach 2) and observed yields for Davié (a), Kumasi (b) and Nyankpala (c). Input variables for Step 3 were the observed nutrient uptakes. HI values were set at 0.50 for Davié and at 0.65 for Kumasi and Nyankpala. Each point represents the average yield of four replicates.

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Fig. 3.5. Yields calculated on the basis of estimated soil and input supplies of nutrients in relation to observed yields in Davié (a), Kumasi (b) and Nyankpala (c). Each point represents the average yield of four replicates.

The comparison of PhE values using an hypothetical cultivar with an HI value of 0.4 (Table 3.5) to those reported under Indian agro-ecological conditions by Byju et al. (2012) revealed that PhE values are higher in India, especially for P, pointing to stronger P dilution than in West Africa. Only PhEKmax was higher in West Africa, reflecting poor K availability, which was especially evident on the Ferralsols in Davié (Fig. 3.3).

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3.3.1.5. Yields in relation to the total supply of available nutrients (Steps 1 - 4) Using the calibrated QUEFTS (PhEmin, PhEmax and HI; Table 3.5), SAβ and MRF values (Table 3.3), the best fit between observed and simulated yields were obtained at Davié (Fig. 3.5). At Kumasi, simulated and observed yields agreed better in 2008 than in 2009 (Fig. 3.5) when observed yields were smaller than calculated yields. The smaller observed yields in 2009 compared to 2008 were likely due to smaller amounts and inadequate distribution of rainfall in 2008. About 49% of total rainfall in the growing season (Table 3.1) occurred in the first month after planting (not shown). Most of this water was likely lost through evaporation as soil coverage by cassava was small in the first month after planting. At Nyankpala, calculated yields were strongly overestimated in both years (Figs 3.4 & 3.5). As suggested above, the growth conditions in Nyankpala during the first part of the growing seasons allowed the crop to take up available nutrients, while drought likely limited growth later in the season, strongly affecting root biomass.

3.3.2. Model testing

Calculated yields agreed well with observed yields (Fig. 3.6). This indicates that the model can effectively estimate cassava response to fertilizer N, P and K (Fig. 3.6a), provided that SAβ values are estimated in such a way to adequately assess yields on control plots. However, the use of site specific MRF values improved the similarity (Fig. 3.6b), indicating that the difference between calculated and observed yields were at least partly due to differences in MRF values between sites.

Fig. 3.6. Calculated yields in relation to observed yields in the model verification trials with common MRF values (a) or adjusted per site (b). Input variables for Step 1 were estimated soil supplies of available nutrients of Table 3.7 and maximum recovery fractions of Table 3.3 (Fig. 3.6a) and Table 3.7 (Fig. 3.6b). Each point represents the average yield of two to five replicates.

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Table 3.7. Soil supplies of available N, P and K (SAβ), yields from control plots without fertilizer application (Y0) in the verification experiment, and the apparent maximum recovery fractions of fertilizer nutrients (MRFβ) estimated with the help of the model (Table 3.5).

Sites Y0 SAβ, kg ha−1 MRFβ

kg ha−1 _{N P K N P K}

Gbave 7682 170 23 67 0.95 0.60 0.95

Davié Tekpo 11801 250 34 99 0.95 0.60 0.95

Sevekpota Black Soil 8728 186 25 74 0.69 0.44 0.80

Sevekpota White Soil 5752 122 17 48 0.81 0.51 0.80

Sevekpota Red Soil 6927 147 20 58 0.69 0.44 0.80

Average Togo 8178 175 24 69 0.82 0.52 0.86 Gbanlahi 7955 74 15 89 0.69 0.21 0.46 Savelegu 12190 113 24 136 0.64 0.20 0.43 Average Ghana 10073 93 20 113 0.66 0.20 0.45 General average 9125 134 22 91 0.74 0.36 0.65 3.4. Discussion

This paper showed that the model can accurately estimate cassava yields when SAβ and MRFβ are accurately assessed and that PhEβ is estimated based on HI in areas where HI is very variable. The use of equations in the original (Janssen and Guiking 1990) and modified (Sattari et al. 2014) versions of QUEFTS underestimated SAβ because such relationships were described for non-irrigated cereal crops. There are two probable causes why the QUEFTS equations did not work for cassava. Firstly, the growth period of cassava is much longer than that of cereals, allowing nutrient uptake over a prolonged period. Secondly, cassava is more effective than cereals in the uptake of P from P-limited soils due to cassava’s strong mycorrhizal symbiosis in its roots (Kang and Okeke 1984; Sieverding and Leihner 1984).

The derivation of SAβ from graphs of the measured maximum uptakes versus the application rate of the concerned nutrient provided a better estimate of SAβ. Estimated SAβ values reflected differences between sites, especially for N and K. The largest value of SAβ for N (SAN) was obtained at Davié, rather than Kumasi which had larger SOC, because Kumasi had larger PhE N for the same amount of N uptake (Fig 3.1a). The highest SAK was estimated at Nyankpala, because of the high availability of K in the soil (Table 3.2). Similar SAP values were obtained across all sites since all sites were poor in available P.

Estimated MRF values reflected soil nutrient availability across sites. The strong K deficiency explained the high MRF of K at Davié. The large SOC at Kumasi with large

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soil N supply resulted in a relatively small MRF of N at this site. The MRF of P varied across sites, with the smallest value obtained at Nyankpala and the largest at Davié. Since all sites had soils with low available P, the difference in MRF of P may be attributed to differences in P requirements to meet the yield potential across sites, and to mycorrhizal enhancing effects on P use efficiency of cassava (Kang and Okeke 1984; Sieverding and Leihner 1984).

The evaluation of the relationships between nutrient uptakes and yields of cassava showed that accurate estimates of nutrient uptakes resulted in accurate assessments of yields in Davié and Kumasi (Fig. 3.4). This suggests that relationships characterized by PhEmax, PhEmin and HI (Equations 3.6 and 3.7) provided a satisfying description of reality. The situation was different at Nyankpala where QUEFTS-calculated yields were one and a half times larger than observed yields, which can be ascribed to the occurrence of drought while the crop was still in the active vegetative stage (Alves 2002). This can also be attributed to nutrient deficiencies (other than N, P and K): the small concentration of magnesium (4.9 mmol kg−1_{) below the critical value of 6.0} mmol kg−1 for cassava (Snapp 1998), could have contributed to the overall weak response of cassava at this site. Strong yield responses to magnesium were obtained in Colombia on depleted soils (CIAT 1985).

The comparison of the studied cultivars with the Indian cultivars used by Byju et al. (2012) on the basis of an HI value of 0.40 revealed that our cultivars had lower PhEmax for P and higher PhEmax for K (Table 3.5). In other words they diluted less P and more K than the Indian cultivars. This suggests that the physiological use efficiency of P can be further improved in West Africa. It also suggests that K deficiency is apparent at the study sites, such as on the Ferralsols in Davié, as also demonstrated in Southern Benin (Carsky and Toukourou 2005).

Calculated yields were close to observed values in the model testing experiments (Fig. 3.6). With SAβ estimates set at a value that QUEFTS compared best to observed control plot yields, the model was able to properly predict cassava responses to combined N, P and K applications. The absence of plant and soil chemical analyses data to derive SAβ is common in sub-Saharan Africa. The method used in this paper of deriving SAβ from control plots without fertilizer can be used when observed yield data from these plots are available. In case yields and plant N, P and K content data from nutrient omission trials (Dobermann et al. 2002; Witt et al. 1999) are available (but no soil chemical data), the method used in the model parameterization trial in this paper can also be applied. However, the availability of plant and soil chemical data is fundamental to be able to relate SAβ to soil parameters as in Step 1 equations of the original version of QUEFTS. The calculations were further improved by use of site

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specific MRF values (Fig. 3.6b), highlighting the importance of location specific soil nutrient management for cassava production.

3.5. Conclusions

The QUEFTS procedures proved useful to estimate cassava yield and responses to mineral fertilizers under rain-fed conditions in West Africa. In years with normal rainfall, the model calculations produced yield estimates close to those observed, but the model overestimated yields under drought conditions. While the current model could be improved with further model testing experiments in other locations in West Africa and with the development of equations for estimating SAβ to cassava based on soil properties, it provides an accurate tool for estimating cassava yield response to fertilizer applications. The strong crop responses to N, P and K highlight the importance of replenishing soil nutrients through external nutrient supplies in cassava production systems. Moreover, our study confirmed the relevance of relating the estimate of PhE for maximum accumulation and maximum dilution to HI when cultivars with different HI are used. Since PhE increased with HI, plant breeders should work towards developing cultivars with higher HI to enhance nutrient use efficiency and yields in cassava production systems in West Africa.

Acknowledgements

We are grateful to many researchers and support staff that contributed in different ways for the successful completion of this project funded by DGIS through the SAADA project implemented by the International Fertilizer Development Centre (IFDC).

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